Multi-Page Printing

You have printed 0 times in the last 24 hours.
Your print count will reset on at .
You may print 0 more time(s) before then.
You may print a maximum of 0 pages at a time.

Number of pages to print:

NOTE: Printing will start on the current page.
Firefox users may need to click "Back" when printing completes.

Combinatorial Game Theory
Page1(16 of 541)

Chapter I Combinatorial Games 1. Introduction Combinatorial games are two-player games with no hidden information and no chance elements. They include child’s play such as Tic-Tac-Toe and Dots and Boxes; mathematical abstractions “played” on arbitrary graphs or grids or posets; and some of the deepest and best-known board games in the world, such as Go and Chess. The mathematical theory of combinatorial games pursues several inter- related objectives, including: • exact solutions to particular games, usually in the form of an algebraic description of their outcomes; • an understanding of the general combinatorial structure of games; and • hardness results, suggesting that for certain games, or in certain situ- ations, no concise solution exists. In all of the games considered in this book, there will be just two players, Left and Right, who play alternately and whose moves aﬀect the position in a manner deﬁned by the rules of the game. Both players will have com- plete knowledge of the game state at all times (“no hidden information”), and the eﬀect of each move will be entirely known before the move is made (“no chance elements”). We’ll defer a formal deﬁnition until after we’ve introduced some examples. 1